(\partial)/(\partial x)(9xe^{6xy})

Lösung

\frac{\partial}{\partial x} (9 x e^{6 x y})

9 (e^{6 x y} + 6 e^{6 x y} x y)

Schritte zur Lösung

\frac{\partial}{\partial x} (9 x e^{6 x y})

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 9 \frac{\partial}{\partial x} (x e^{6 x y})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{6 x y}

= 9 (\frac{\partial}{\partial x} (x) e^{6 x y} + \frac{\partial}{\partial x} (e^{6 x y}) x)

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (e^{6 x y}) = e^{6 x y} \cdot 6 y

= 9 (1 \cdot e^{6 x y} + e^{6 x y} \cdot 6 y x)

Vereinfache

= 9 (e^{6 x y} + 6 e^{6 x y} x y)

(3 x + 2 y + 1) d x - (3 x + 2 y - 1) d y = 0

\int (x + 2 + \frac{3}{x}) d x

\int_{0}^{π} sec^{2} (\frac{x}{3}) d x

e^{- x} y \frac{d y}{d x} = e^{- y} + e^{- 2 x - y}

\int \frac{4 e ^{3 x}}{1 + e ^{3 x}} d x